Original scientific paper

https://doi.org/10.31896/k.21.4

Non-standard Aspects of Fibonacci Type Sequences

Gunter Weiss ; University of Technology Vienna, University of Technology Vienna,University of Technology Vienna,Vienna, Austria

Abstract

Fibonacci sequence and the limit of the quotient of adjacent Fibonacci numbers, namely the Golden Mean, belong to general knowledge of almost anybody, not only of mathematicians and geometers. There were several attempts to generalize these fundamental concepts which also found applications in art and architecture, as e.g. number series and quadratic equations leading to the so-called ˝Metallic means" by V. DE SPINADEL [8] or the cubic ˝plastic number" by VAN DER LAAN [5] resp. the ˝cubi ratio" by L. ROSENBUSCH [7]. The mentioned generalisations consider series of integers or real numbers. ˝Non-standard aspects" now mean generalisations with respect to a given number field or ring as well as visualisations of the resulting geometric objects. Another aspect concerns Fibonacci type resp. Padovan type combinations of given start objects. Here it turns out that the concept ˝Golden Mean" or ˝van der Laan Mean" also makes sense for vectors, matrices and mappings.

Keywords

generalized Fibonacci sequence; Golden Mean; non-Euclidean geometry; number field; ring

Hrčak ID:

192219

URI

https://hrcak.srce.hr/192219

Publication date:

9.1.2018.

Article data in other languages: croatian

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